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Intermediate Geometry : How to find the endpoints of a line segment

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Example Questions

Example Question #45 : Midpoint Formula

A line segment has an endpoint at (11, -2) and a midpoint at (5, 0) . Find the coordinates of the other endpoint.

Possible Answers:

(2, 1)

(-1, 2)

(-1, 0)

(3, -2)

Correct answer:

(-1, 2)

Explanation:

Recall how to find the midpoint of a line segment:

$\text{Midpoint}=(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})$ ,

where $(x_1, y_1)\text{ and}(y_1, y_2)$ are the endpoints.

Let's first focus on the coordinate of the other endpoint. Using the information given by the question, we can write the following equation:

$\frac{11+x_2}{2}=5$

Solve for x_2 .

11+x_2=10

x_2=-1

Next, find the coordinate of the other endpoint. Using the information given by the question, we can write the following equation:

$\frac{-2+y_2}{2}=0$

-2+y_2=0

y_2=2

The second endpoint must be at (-1, 2) .

Report an Error

Example Question #46 : Midpoint Formula

A line segment has an endpoint at (-24, 12) and midpoint at (30, -5) . Find the coordinates of the other endpoint.

Possible Answers:

(90, -24)

(92, -15)

(80, -40)

(84, -22)

Correct answer:

(84, -22)

Explanation:

Recall how to find the midpoint of a line segment:

$\text{Midpoint}=(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})$ ,

where $(x_1, y_1)\text{ and}(y_1, y_2)$ are the endpoints.

Let's first focus on the coordinate of the other endpoint. Using the information given by the question, we can write the following equation:

$\frac{-24+x_2}{2}=30$

Solve for x_2 .

-24+x_2=60

x_2=84

Next, find the coordinate of the other endpoint. Using the information given by the question, we can write the following equation:

$\frac{12+y_2}{2}=-5$

12+y_2=-10

y_2=-22

The second endpoint must be at (84, -22) .

Report an Error

Example Question #47 : Midpoint Formula

A line segment has an endpoint at (1, 7) and midpoint at (5, 0) . Find the coordinates of the other endpoint.

Possible Answers:

(9, -7)

(8, -6)

(10, -2)

(12, -9)

Correct answer:

(9, -7)

Explanation:

Recall how to find the midpoint of a line segment:

$\text{Midpoint}=(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})$ ,

where $(x_1, y_1)\text{ and}(y_1, y_2)$ are the endpoints.

Let's first focus on the coordinate of the other endpoint. Using the information given by the question, we can write the following equation:

$\frac{1+x_2}{2}=5$

Solve for x_2 .

1+x_2=10

x_2=9

Next, find the coordinate of the other endpoint. Using the information given by the question, we can write the following equation:

$\frac{7+y_2}{2}=0$

7+y_2=0

y_2=-7

The second endpoint must be at (9 -7) .

Report an Error

Example Question #48 : Midpoint Formula

A line segment has an endpoint at (-2, 5) and midpoint at (11, 2) . Find the coordinates of the other endpoint.

Possible Answers:

(24, -1)

(26, -10)

(19, 1)

(22, -2)

Correct answer:

(24, -1)

Explanation:

Recall how to find the midpoint of a line segment:

$\text{Midpoint}=(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})$ ,

where $(x_1, y_1)\text{ and}(y_1, y_2)$ are the endpoints.

Let's first focus on the coordinate of the other endpoint. Using the information given by the question, we can write the following equation:

$\frac{-2+x_2}{2}=11$

Solve for x_2 .

-2+x_2=22

x_2=24

Next, find the coordinate of the other endpoint. Using the information given by the question, we can write the following equation:

$\frac{5+y_2}{2}=2$

5+y_2=4

y_2=-1

The second endpoint must be at (24, -1) .

Report an Error

Example Question #49 : Midpoint Formula

A line segment has an endpoint at (-2, -4) and midpoint at (-5, 0) . Find the coordinates of the other endpoint.

Possible Answers:

(-10, 8)

(-8, 4)

(2, 4)

(-12, 12)

Correct answer:

(-8, 4)

Explanation:

Recall how to find the midpoint of a line segment:

$\text{Midpoint}=(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})$ ,

where $(x_1, y_1)\text{ and}(y_1, y_2)$ are the endpoints.

Let's first focus on the coordinate of the other endpoint. Using the information given by the question, we can write the following equation:

$\frac{-2+x_2}{2}=-5$

Solve for x_2 .

-2+x_2=-10

x_2=-8

Next, find the coordinate of the other endpoint. Using the information given by the question, we can write the following equation:

$\frac{-4+y_2}{2}=0$

-4+y_2=0

y_2=4

The second endpoint must be at (-8, 4) .

Report an Error

Example Question #50 : Midpoint Formula

A line segment has an endpoint at (3, 16) and midpoint at (14, 7) . Find the coordinates of the other endpoint.

Possible Answers:

(27, -3)

(25, -2)

(2, -12)

(15, -2)

Correct answer:

(25, -2)

Explanation:

Recall how to find the midpoint of a line segment:

$\text{Midpoint}=(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})$ ,

where $(x_1, y_1)\text{ and}(y_1, y_2)$ are the endpoints.

Let's first focus on the coordinate of the other endpoint. Using the information given by the question, we can write the following equation:

$\frac{3+x_2}{2}=14$

Solve for x_2 .

3+x_2=28

x_2=25

Next, find the coordinate of the other endpoint. Using the information given by the question, we can write the following equation:

$\frac{16+y_2}{2}=7$

16+y_2=14

y_2=-2

The second endpoint must be at (25, -2) .

Report an Error

Example Question #51 : Midpoint Formula

A line segment has an endpoint at (8, -2) and midpoint at (1, -1) . Find the coordinates of the other endpoint.

Possible Answers:

(2, 0)

(-5, 0)

(-6, 0)

(2, 10)

Correct answer:

(-6, 0)

Explanation:

Recall how to find the midpoint of a line segment:

$\text{Midpoint}=(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})$ ,

where $(x_1, y_1)\text{ and}(y_1, y_2)$ are the endpoints.

Let's first focus on the coordinate of the other endpoint. Using the information given by the question, we can write the following equation:

$\frac{8+x_2}{2}=1$

Solve for x_2 .

8+x_2=2

x_2=-6

Next, find the coordinate of the other endpoint. Using the information given by the question, we can write the following equation:

$\frac{-2+y_2}{2}=-1$

-2+y_2=-2

y_2=0

The second endpoint must be at (-6, 0) .

Report an Error

Example Question #52 : Midpoint Formula

A line segment has an endpoint at (9, -3) and midpoint at (12, -8) . Find the coordinates of the other endpoint.

Possible Answers:

(16, -21)

(17, -18)

(15, -13)

(19, -4)

Correct answer:

(15, -13)

Explanation:

Recall how to find the midpoint of a line segment:

$\text{Midpoint}=(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})$ ,

where $(x_1, y_1)\text{ and}(y_1, y_2)$ are the endpoints.

Let's first focus on the coordinate of the other endpoint. Using the information given by the question, we can write the following equation:

$\frac{9+x_2}{2}=12$

Solve for x_2 .

9+x_2=24

x_2=15

Next, find the coordinate of the other endpoint. Using the information given by the question, we can write the following equation:

$\frac{-3+y_2}{2}=-8$

-3+y_2=-16

y_2=-13

The second endpoint must be at (15, -13) .

Report an Error

Example Question #53 : Midpoint Formula

A line segment has an endpoint at (17, 2) and midpoint at (6, 8) . Find the coordinates of the other endpoint.

Possible Answers:

(18, 17)

(18, 20)

(16, 12)

(15, 14)

Correct answer:

(15, 14)

Explanation:

Recall how to find the midpoint of a line segment:

$\text{Midpoint}=(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})$ ,

where $(x_1, y_1)\text{ and}(y_1, y_2)$ are the endpoints.

Let's first focus on the coordinate of the other endpoint. Using the information given by the question, we can write the following equation:

$\frac{17+x_2}{2}=6$

Solve for x_2 .

17+x_2=32

x_2=15

Next, find the coordinate of the other endpoint. Using the information given by the question, we can write the following equation:

$\frac{2+y_2}{2}=8$

2+y_2=16

y_2=14

The second endpoint must be at (15, 14) .

Report an Error

Example Question #54 : Midpoint Formula

A line segment has an endpoint at (-2, 4) and a midpoint at (12, 2) . Find the other endpoint.

Possible Answers:

(30, 4)

(28, -2)

(-14, 22)

(26, 0)

Correct answer:

(26, 0)

Explanation:

Recall how to find the midpoint of a line segment:

$\text{Midpoint}=(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})$ ,

where $(x_1, y_1)\text{ and}(y_1, y_2)$ are the endpoints.

Let's first focus on the coordinate of the other endpoint. Using the information given by the question, we can write the following equation:

$\frac{-2+x_2}{2}=12$

Solve for x_2 .

-2+x_2=24

x_2=26

Next, find the coordinate of the other endpoint. Using the information given by the question, we can write the following equation:

$\frac{4+y_2}{2}=2$

4+y_2=4

y_2=0

The second endpoint must be at (26, 0) .

Report an Error

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Intermediate Geometry : How to find the endpoints of a line segment

Study concepts, example questions & explanations for Intermediate Geometry

All Intermediate Geometry Resources

Example Questions

Example Question #45 : Midpoint Formula

Example Question #46 : Midpoint Formula

Example Question #47 : Midpoint Formula

Example Question #48 : Midpoint Formula

Example Question #49 : Midpoint Formula

Example Question #50 : Midpoint Formula

Example Question #51 : Midpoint Formula

Example Question #52 : Midpoint Formula

Example Question #53 : Midpoint Formula

Example Question #54 : Midpoint Formula

All Intermediate Geometry Resources

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